Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Sivaraman, Vaidyanathan
Committee Member
Fabel, Paul
Committee Member
Qian, Chuanxi
Committee Member
Yarahmadian, Shantia
Date of Degree
8-8-2023
Document Type
Dissertation - Open Access
Major
Mathematical Science
Degree Name
Doctor of Philosophy (Ph.D)
College
College of Arts and Sciences
Department
Department of Mathematics and Statistics
Abstract
In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate the absence of sign-symmetric signed graphs in some cases. We then introduce and study the signed graph class $\mathcal{S}$, which includes all sign-symmetric signed graphs, we prove several theorems and lemmas as well as discuss the class of tangled sign-symmetric signed graphs. Also, we study the graph class $\mathcal{G}$, consisting of graphs with at least one sign-symmetric signed graph, prove additional theorems and lemmas, and determine certain families within $\mathcal{G}$. Our results have practical applications in various fields such as social psychology and computer science.
Recommended Citation
Asiri, Ahmad, "Signings of graphs and sign-symmetric signed graphs" (2023). Theses and Dissertations. 5973.
https://scholarsjunction.msstate.edu/td/5973
Included in
Discrete Mathematics and Combinatorics Commons, Geropsychology Commons, Graphics and Human Computer Interfaces Commons, Other Mathematics Commons, Social Psychology Commons, Theory and Algorithms Commons